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amrexpr: AMReX's Mathematical Expression Parser

Overview

This is a standalone mathematical expression parser library extracted from the AMReX software framework. AMReX is designed for high-performance computing applications that solve partial differential equations on block-structured adaptive meshes. This library is for users who wish to utilize the parser functionality without incorporating the full AMReX framework. It supports both CPU and GPU architectures, including Nvidia, AMD, and Intel GPUs. It requires C++17 or later.

Features

The parser can be used at runtime to evaluate mathematical expressions given in the form of string. It supports +, -, *, /, ** (power), ^ (power), sqrt, exp, log, log10, sin, cos, tan, asin, acos, atan, atan2, sinh, cosh, tanh, asinh, acosh, atanh, abs, floor, ceil, fmod, and erf. The minimum and maximum of two numbers can be computed with min and max, respectively. It supports the Heaviside step function, heaviside(x1,x2) that gives 0, x2, 1, for x1 < 0, x1 = 0 and x1 > 0, respectively. It supports the Bessel function of the first kind of order n jn(n,x). Complete elliptic integrals of the first and second kind, comp_ellint_1(k) and comp_ellint_2(k), are supported. There is if(a,b,c) that gives b or c depending on the value of a. A number of comparison operators are supported, including <, >, ==, !=, <=, and >=. The Boolean results from comparison can be combined by and and or, and they hold the value 1 for true and 0 for false. The precedence of the operators follows the convention of the C and C++ programming languages. Here is an example of using the parser.

   #include "amrexpr.hpp"

   Parser parser("if(x>a and x<b, sin(x)*cos(y)*if(z<0, 1.0, exp(-z)), .3*c**2)");
   parser.setConstant(a, ...);
   parser.setConstant(b, ...);
   parser.setConstant(c, ...);
   parser.registerVariables({"x","y","z"});
   auto f = parser.compile<3>();  // 3 because there are three variables.

   // f can be used in both host and device code.  It takes 3 arguments in
   // this example.  The parser object must be alive for f to be valid.
   for (int k = 0; ...) {
     for (int j = 0; ...) {
       for (int i = 0; ...) {
         a(i,j,k) = f(i*dx, j*dy, k*dz);
       }
     }
   }

Local automatic variables can be defined in the expression. For example,

   Parser parser("r2=x*x+y*y; r=sqrt(r2); cos(a+r2)*log(r)"
   parser.setConstant(a, ...);
   parser.registerVariables({"x","y"});
   auto f = parser.compile<2>();  // 2 because there are two variables.

Note that an assignment to an automatic variable must be terminated with ;, and one should avoid name conflict between the local variables and the constants set by setConstant and the variables registered by registerVariables.

Installation

There two ways to install amrexpr. A simple example demonstrating the use of libamrexpr is available at amrexpr/Tutorials/libamrexpr.

Option 1: Using GNU Make

In the amrexpr root directory, follow these steps:

$ ./configure
$ make -j8
$ make install

To see the list of options, run ./configure -h. These options allow you to configure installation directory, choose the compiler, specify GPU backends, and more.

Option 2: Using CMake

To build for CPUs, follow these steps in the amrexpr root directory:

$ cmake -S . -B build -DCMAKE_INSTALL_PREFIX=<installation_direction>
$ cmake --build build -j 8
$ cmake --install build

To build for GPUs, we use the ENABLE_[CUDA|HIP|SYCL] option and specify the GPU architecture in the configure step. For example

# Nvidia GPU w/ compute capability 8.0
$ cmake -S . -B build -DCMAKE_INSTALL_PREFIX=<installation_direction> \
      -DENABLE_CUDA=ON -DCMAKE_CUDA_ARCHITECTURES=80

# AMD MI250X GPU, gfx90a architecture
$ cmake -S . -B build -DCMAKE_INSTALL_PREFIX=<installation_direction> \
      -DENABLE_HIP=ON -DCMAKE_HIP_ARCHITECTURES=gfx908

# Intel GPU
$ cmake -S . -B build -DCMAKE_INSTALL_PREFIX=<installation_direction> \
      -DENABLE_SYCL=ON -DCMAKE_CXX_COMPILER=icpx

Copyright Notice

AMReX Copyright (c) 2024, The Regents of the University of California, through Lawrence Berkeley National Laboratory (subject to receipt of any required approvals from the U.S. Dept. of Energy). All rights reserved.

If you have questions about your rights to use or distribute this software, please contact Berkeley Lab's Intellectual Property Office at IPO@lbl.gov.

Please see the notices in NOTICE.

License

License for AMReX can be found at LICENSE.